Abstract

The monoid Fn of uniform block bijections is the factorizable inverse monoidwhich arises from the natural action of the symmetric group on the joinsemilattice of equivalences on an n-set; it has been described in the literature as the factorizable part of the dual symmetric inverse monoid. Thepresent paper gives and proves correct a monoid presentation for Fn: Themethods involved make use of a general criterion for a monoid generated bya group and an idempotent to be inverse, the structure of factorizable inversemonoids, and presentations of the symmetric group and the join semilatticeof equivalences on an n-set.

Different title on PDFA presentation for the monoid of uniform block bijections

This is the author's preprint version, which differs from the published version in having an older address, and omitting an introductory paragraph and a reference, added in proof, to M. Kosuda, Ryuku Math. J.13 (2000) 7-22.